A. Verify Clairaut's Theorem for the given function: F(U,W) = Sin(UW)- 4U?w2 %3!

Q: What is the direction in which the function f(x, y) = yx - increases most rapidly at the point (-2,…

A: Given: f(x,t)=yx2-x/y2      at (-2,1)

Q: Complete the table by "breaking down"the function into the inner"and "outer" Function dy du dy u du…

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Q: Find f.  f''(t)=sin t + cos t,    f(0)=2,    f'(0)=4f f(t)= ?

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Q: The temperature in Edmonton, over the course of a year, can be approximated using the sinusoidal…

A: The given sinusoidal function is: Tx=16.11sin0.51x-1.75+9.14   ......(1)where T is the temperature…

Q: Let y = (sin x+ cos r)e , x E 0, 27. Then the x coordinates of the inflection point(s) of this…

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Q: Find the local extrema of the function f(x, y) = e-(cos(r)+sin(y)) and test for which are max, min,…

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Q: d Find the value of f(t) if f(t) : sin(Vx) dx. dt. f(t) %3D

A: here use the fundamental theorem of calculus

Q: Find L[f]for each f(t). Q) f(t)=eat sin bt, where a,b are constants.

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Q: - fyr. For the function f(x, y) = e²´y sin(xy) show that Clairaut's Theorem holds, that is, fæy

A: Clairut's Theorem : fxy = fyx i.e, ∂2f∂x∂y =∂2f∂y∂x.

Q: Let f(z) = V sin(e=*cos(=)) f'(x) =0

A: We need to find derivative.

Q: The domain of the function y tanh z is 1, +∞). Select one: a. False Ob. True

A: To find the domain of this function, we use the fact that for any one-to-one invertible function f…

Q: Determine frx and fry for the function below: f (x, y) = x²y + y cos x – e*y In((y) + 7. -

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Find the directional derivative of Du" f (2,1) in the direction of: a = 3i + 4j To f(x, y) = InGes…

A: Gradient of a function :  Let f be a differentiable function at  x , y  and let f x , y  have…

Q: Determine the equation of the tangent to fr) = x + x at the point (1, 2). %3D O a) y = 3x - 1 %3D b)…

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Q: COS Z fined the Res of the function T Z 4 -

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Q: (c) Differentiate the following functions with respect to x. (i) х3 + 5y4 — 2 — 1. (ii) y = -…

A: Differentiate the given functions with respect to x.

Q: B) Find- for following functions: дz მა 1) z = exy tan y, x = s + 2t, y = s/t. 2) z = x² + xy + y²,…

A: The objective of the question is evaluate the partial derivative of the given functions.

Q: бл Approximate sin by using a linear approximation with f(x) = sin x. 13 (等) z f(a) + f ' (a)·h = c,…

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Q: Assuming 8x - y +7xy = 0 defines y as a differentiable function of x, use the theorem dx Fx to find…

A: By using partial differentiation .

Q: Use Euler’s method to approximate the indicated function value to 3 decimal places, using h =   0.1.

A: Use Euler’s method to approximate the indicated function value to 3 decimal places, using h =   0.1.…

Q: Find f. f "(t) = 5e + 8 sin t, f(0) = 0, f(x) = 0 f(t) :

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Q: A. Find the derivative of the function at o P in the direction of A f(x, у) — х — V3sec-1(2xy)at…

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Q: Use convolutions to find an explicit function y(t) such that pt y(t) = 1+ | y(t) sin(t – æ) dæ.

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Q: J (X, 0 defineš z implicitly as a function of and #0. dz ye"-9 sin 4z = 4z %3D dz az %3D dy

A: The objective is to find the partial derivatives.

Q: 19. Differentiate the following functions. c) y = Vx ++ Vã sec (x³+1) cos ya d) y =

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Q: Find the linear approximation to f(x)= cot (x) LCx) = f (a) + f'Ca) (x-a). near a=" as

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Q: Find the slope of the tangent line of the function y = In (x) at x = e2 O1/e? 4/et O 1/e* O 2le2

A: Topic = Derivative As per guidelines, At a time only one question can be answered out of different…

Q: i f(t) is given E ue of f(0.5) is

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Q: The tangent line to the curve y=f(x) is horizontal at where X = Xo f f(xx) = 00 A O f(xo) = 00 .8 O…

A: The tangent line to the curve y=f(x) is horizontal at where x=x0 if

Q: a) Find the derivative of f(x,y) = xe* +cos(xy) at the point (2,0) in the direction of V = 3i – 4 j.

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Q: (a) Let f(z) = sin*(z). Find f' (x), T(2) = (b) Let f(x) = J (x) = sin(z³). Find f'(x). %3D

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Q: At what points are the functions continuous?

A: The function can not have a negative value under a square root.  But x^4+1 > 0 for all values of…

Q: Given f(x, y, z) = xe"y + sin(xyz), find fyzz

A: Derivatives of: Sin x is Cos x Cos x is -Sin x u

Q: Q3) for f(t) = sec?(6t – 1) and g(t) = tan?(6t - 1) show that %3D f'(t) = g'(t).

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Q: Verify that the conclusion of Clairaut's Theorem holds for the function: f (x, y) = e*y sin(y)

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Q: f (x) = sec? x +1

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Q: Let f(x)= sec(x), find the linear approximation at x= pi/4 and use it to estimate sec(pi/5)

A: Given function: fx=secx At x=π4 fπ4=secπ4=2

Q: Consider the function f defined by f(x,t) = sin (x) exp(t) fi(x,t)+ fr»(x,t) =

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Q: Differentiate the following function. r(t) = (te ~!,5t In t,t sin t)

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Q: Evaluate the given function using homogeneous ydx = (x y² – x² dy) A. Arcsin () = = In B. Arctan (-)…

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Q: Consider the function f defined by f(x,t) cos(r) exp(t)

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Q: Find f. f '(t) = 2 cos t + sec?t, , -1/2 < t < «/2, _f(x/3) = 3 f(t) =

A: Given: The derivative function f'(t)=2cost+sec2t , -π2&lt;t&lt;π2 , fπ3=3. To find :  The function…

Q: Exercise 11. For what values of p is the function f(x) = { {JzP sin (!) x #0 x = 0 0 differentiable?

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Q: Consider the function g(x) = 5 S cos t dt – x?. Then g' (x) is

A: Given gx=12∫x4x2costdt  -x2

Q: Given the implicitly defined function sin(r²y³) + y³ = r + y I dy dy and dx2 find at the point (x,…

A: Topic = Derivative

Q: Differentiate the function. F(t) = e6t sin(2t) F'(t) =

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Q: ind the linear approximation of the function at the given point. x_ v) = -4 sinx+ 7 cos y at (0, 7…

A: Hey, Since you have posted multiple questions we will answer only first question.

Q: It is definend as (Tf) (t) = S sin?(x – t)f(t)dx ,with fe [0,1] 1) is T: c [0,1] → c [0,1] defined…

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Q: Verify the condition of Rolle's theorem for the function y = f(x) = e xe[-1] ] f'(c) = 0 and find C…

A: Rolle's theorem: If f(x) is a real-valued function defined on a,b such that; 1). f(x) is continuous…

Q: For what value(s) of x in the interval -15 sxs -5 will the sinusoidal function shown below have a…

A: By definition, a function is a special case of a relation between the members of two sets. It is a…